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International Computing and Combinatorics Conference

COCOON 2017: Computing and Combinatorics pp 275–286Cite as

Unfolding Some Classes of Orthogonal Polyhedra of Arbitrary Genus

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10392))

Abstract

Unfolding polyhedra beyond genus zero (i.e., with holes) is challenging, yet it has not been investigated until very recently. We show two types of orthogonal polyhedra of arbitrary genus, namely, well-separated orthographs and regular orthogonal polyhedra with x- and z-holes, to enjoy \((2 \times 1)\)-grid-unfoldings, generalizing some prior work in the literature by allowing holes (or more complicated holes) to exist. In addition to the development of new unfolding techniques, for the first time we identify classes of nontrivial orthogonal polyhedra of arbitrary genus to admit grid-unfoldings subject to a small amount of refinements.

H.-C Yen—Research supported in part by Ministry of Science and Technology, Taiwan, under grant MOST 103-2221-E-002-154-MY3.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan

    Kuan-Yi Ho & Hsu-Chun Yen

  2. Department of EECS, University of Michigan, Ann Arbor, MI, USA

    Yi-Jun Chang

Authors
  1. Kuan-Yi Ho
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  2. Yi-Jun Chang
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  3. Hsu-Chun Yen
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Corresponding author

Correspondence to Hsu-Chun Yen .

Editor information

Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. Texas A&M University, College Station, Texas, USA

    Jianer Chen

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© 2017 Springer International Publishing AG

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Ho, KY., Chang, YJ., Yen, HC. (2017). Unfolding Some Classes of Orthogonal Polyhedra of Arbitrary Genus. In: Cao, Y., Chen, J. (eds) Computing and Combinatorics. COCOON 2017. Lecture Notes in Computer Science(), vol 10392. Springer, Cham. https://doi.org/10.1007/978-3-319-62389-4_23

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  • DOI: https://doi.org/10.1007/978-3-319-62389-4_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62388-7

  • Online ISBN: 978-3-319-62389-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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